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中文摘要：
设{εt，t∈Z}为定义在同一概率空间（Ω，f,p）上的严平稳随机变量序列，满足Eε0=0，E｜ε0｜^p〈∞，对某个p〉2，且满足强混合条件．{aj，j∈Z}为一实数序列，满足^∞∑j=-∞ ｜aj｜〈∞,^∞∑j=-∞ a≠0．令Xt=^∞∑ j=-∞ ajε（t-j）（t≥1），Sn=^n∑t=1 Xt（n≥1）．利用由强混合序列生成的线性过程的弱收敛定理及矩不等式讨论了在bn=0（1／log log n）的条件下，当∈→0时，P{｜Sn｜≥（∈＋bb）τ√2nlog log n }的一类加权级数的收敛性质．
英文摘要：
Let {εt,t∈Z} be a strictly stationary sequence defined on a probability space （Ω,f,p） such that Eε0=0, and E｜ε0｜^p〈∞, for some p 〉 2. And the sequence {εt,t∈Z}, is assumed to mixing conditions {aj,j∈Z} is a sequence of real numbers with ^∞∑j=-∞ ｜aj｜〈∞,^∞∑j=-∞ a≠0. Xt=^∞∑ j=-∞ ajε（t-j）（t≥1）,Sn=^n∑t=1 Xt（n≥1）. Using the weak convergence theorem of the linear process generated by strong mixing sequences and the moment inequaliti asymptotics of strong mixing sequences, we studied the precise asymptoties of a kind of weighted infinite series of P {｜Sn｜≥（∈＋bb）τ√2nlog log n } as ∈→0 under the conditions of bn=0（1/log log n）.
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